A353779 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + tanh(x).

1, 0, -2, 8, -24, 144, -720, 7552, -35840, 427520, -3628800, 45415424, -479001600, 7094226944, -82614884352, 1741160087552, -20922789888000, 371094631612416, -6402373705728000, 137529198176370688, -2379913632645120000, 55730621780175355904

Offset: 1

Author

Ilya Gutkovskiy, May 08 2022

Keywords

• sign

Crossrefs

Cf. A006973, A137852, A155585, A353607, A353608, A353609, A353610, A353611.

Programs

Mathematica

nn = 22; f[x_] := Product[(1 + a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Tanh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten